The author first inquires into the annual and diurnal variations of the barometer and thermometer, for the determination of which he takes the mean of the observations in each month made at the Apartments of the Royal Society, during the years 1827,1828, and 1829; and also that deduced from Mr. Bouvard’s observations, published in the Memoirs of the French Academy of Sciences. From the table given it would appear that the annual variations are independent of the diurnal variations. A much greater number of observations than we possess at present, made frequently and at stated times each day, are requisite before any very satisfactory conclusion can be deduced as to the influence of the moon on the fluctuations of the barometer. The author, however, has attempted the inquiry, as far as the limited range of the present records will allow, by classifying all the observed heights, corresponding to a particular age of the moon, as defined by her transit taking place within a given half hour of the day; and thence deducing mean results, which are exhibited in tables. The results afforded by the observations at Somerset House differ widely from those obtained from corresponding observations made at the Paris Observatory. According to the former, the barometer is highest at new and full moons, and lowest at the quadratures the extent of the fluctuations being 0.08 of an inch: according to the lottery the controly is the esse, and the extent is only 0.05 of an inch.